I have a Fiskars punch and make my hexie templates out of ads on heavy card stock I get in the mail. I DO remove my templates BEFORE I even sew my flowers together. I spray starch & iron them and have no trouble with them losing their shape.

The last time I did hexies, I used some junk mail that was a bit too stiff for my liking, so I pressed the shapes with a little starch, removed the paper, then I added a dab of glue stick in the seam allowances. It worked like a dream.